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A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 105 ✬ ✫ Klasična definicija verjetnosti Pri določitvi verjetnosti si pri nekaterih poskusih in dogodkih lahko pomagamo s klasično definicijo verjetnosti: Vzemimo, da so dogodki iz popolnega sistema dogodkov {E1, E2, . . . , Es} enako verjetni: P (E1) = P (E2) = . . . = P (Es) = p. Tedaj je P (Ei) = 1/s i = 1, . . . , s. Če je nek dogodek A sestavljen iz r dogodkov iz tega popolnega sistema dogodkov, potem je njegova verjetnost P (A) = r/s. Primer: Izračunajmo verjetnost dogodka A, da pri metu kocke padejo manj kot 3 pike. Popolni sistem enako verjetnih dogodkov sestavlja 6 dogodkov. Od teh sta le dva ugodna za dogodek A (1 in 2 piki). Zato je verjetnost dogodka A enaka 2 6 = 1 3 . Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 106 ✬ ✫ Geometrijska verjetnost V primerih, ko lahko osnovne dogodke predstavimo kot ‘enakovredne’ točke na delu premice (ravnine ali prostora), določimo verjetnost sestavljenega dogodka kot razmerje dolˇzin (ploˇsčin, prostornin) dela, ki ustreza ugodnim izidom, in dela, ki ustreza vsem moˇznim izidom. Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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